In the modern Garmin Connect, click the three horizontal bars icon on the left of the window, then click the word Connections in the popout menu. Find the connection you don't want, then click the dropdown box that says Connected next to the connection you want to remove. Click Disconnect.
From the classic Garmin Connect, click your Garmin Connect username in near the top-right corner of the page. Then select My Connections from the dropdown box. Find the connection you don't want, then click the dropdown box that says Connected next to the connection you want to remove. Click Disconnect.